Two internal friction peaks versus temperature (P′1 and P″1) are previously observed around room temperature in cold‐worked and partially annealed dilute solutions of Al‐Mg. Each peak exhibits an abnormally amplitude‐dependent peak (versus amplitude) having its own characteristic behaviour. The amplitude peak associated with P′1 peak appears at an amplitude range lower than that associated with P″1 peak. Two amplitude peaks are observed in a free decay experiment at different amplitude ranges. Auxiliary experiments show that the double amplitude peaks observed do not result from some sort of coupling between various vibration modes of the pendulum system during internal friction measurements with an inverted torsion pendulum. A mechanism of the double amplitude peaks is suggested in terms of the simultaneous occurrence of longitudinal core diffusion (LCD) and transverse core diffusion (TCD) of the solute atoms during the to and fro sidewise motion of the dislocation kinks.